The (tree) amplituhedron \(\mathcal {A}_{n,k,m}\)  is a subspace of the Grassmannian
\({\rm Gr}_{k,k+m}\)  introduced by Arkani-Hamed and Trnka in [1]}
in order to compute scattering amplitude of a certain quantum field
theory. From the mathematical perspective, it is a generalization
of the totally nonnegative Grassmannian \({\rm Gr}_{k,n}^{\ge 0}\)  with many interesting
properties. For example, in [2]} it is proved
that a certain amplituhedron is homeomorphic to a ball, in [3]}, [4]}, [5]}
results about cell decompositions of the tree amplituhedron are given.
See also [6]} and [7]} for
a description of the tree amplituhedron when \(m=1\)  and \(m=2\) .
